Hi, this is actually for my general relativity class, but I thought I would get more help in the math section of the forums, since it involves very little physics, or even not at all.(adsbygoogle = window.adsbygoogle || []).push({});

1. The problem statement, all variables and given/known data

Take T_{ab}and S_{ab}to be the covariant components of two tensors. Consider the determinant equation for [itex]\lambda[/itex] :

| [tex]\lambda[/tex]T_{ab}- S_{ab}|= 0

Prove that the roots of this equation are scalars, making clear what you mean by scalar.

2. Relevant equations

3. The attempt at a solution

Well If I solve for the determinant I think I should get a quartic equation for the eigenvalues [itex]\lambda[/itex] of the form

[tex]\lambda[/tex]^4 + a_{1}[tex]\lambda[/tex]^3 + a_{2}[tex]\lambda[/tex]^2 + a_{3}[tex]\lambda[/tex] + a_{4}= 0

Or not? Will I get an equation involving the components of the tensors T and S??

I just want to make sure I am understanding the question and I'm headed in the right path.

Any suggestions are greatly appreciated.

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# Homework Help: Eigenvector equation

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